   Chapter 11, Problem 34RE ### Mathematical Applications for the ...

11th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781305108042

#### Solutions

Chapter
Section ### Mathematical Applications for the ...

11th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781305108042
Textbook Problem

# Environment Suppose that in a study of water birds, the relationship between the area A of wetlands (in square miles) and the number of different species S of birds found in the area was determined to be S   =   k A 1 / 3 where k is constant. Find the percent rate of change of the number of species in terms of the percent rate of change of the area.

To determine

To calculate: The percent rate of change of the number of species in terms of the percent rate of the change of area if the study of water birds, shows the relationship between the area A of wetlands(in square miles) and the number of different species S of birds found in the area is determined to be S=kA13.

Explanation

Given Information:

The relationship between the area A of wetlands (in square miles) and the number of different species S of birds found in the area is determined to be S=kA13.

Formula Used:

The power rule of derivative,

ddx(xn)=nxn1

Calculation:

The provided equation is S=kA13,

Differentiate on both the sides with respect to t by the product rule,

ddt(S)=ddt(kA13)=kddt(A13)

Now apply the power rule of derivative,

The percent rate of change is given as,

dSdtS

Divide the equation by S

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